Quote of the Day- The Definition of Equilibrium

"We have not thus far attempted to formulate a definition of equilibrium, though the meaning of the term has probably become quite clear. In the light of the preceding discussion we may define equilibrium, in economic analysis, as a constellation of selected interrelated variables so adjusted to one another that no inherent tendency to change prevails in the model which they constitute. The model as well as its equilibria are, of course, mental constructions (based on abstraction and invention).

It has been suggested to me that the phrase "balance of forces " should be a part of any definition of equilibrium. I cannot accept this suggestion; “ balance of forces " is simply another metaphor, perhaps a synonym but not an explanation of “equilibrium”, and sadly encumbered by the reference to "forces," which is a rather mystical concept in need of a separate time consuming cleaning job. But if it is believed that additional metaphors can be helpful in defining or explaining equilibrium, then I should propose the phrase " peaceful co-existence " between selected variables of given magnitudes. Where such " peaceful co-existence " is not possible, where the selected variables are not compatible with one another in their given magnitudes, one or more of them will have to change, and will continue to change until they reach magnitudes that make it possible for them to live with each other as they are.

Thus, as an alternative definition of equilibrium we may propose mutual compatibility of a selected set of interrelated variables of particular magnitudes. Assume the set consists of variables A, B, C and D, and that certain interrelationships between them are assumed (in the form of behaviour equations, technological, psychological or institutional relations, as well as mere definitions). If these variables are compatible in their " present " magnitudes "everything could go on as it is." Then " something happens " which increases variable C. In its new magnitude C is no longer compatible with A, B and D, and " things must adjust themselves." Which of the variables will "give" and by how much will depend on the rules of the game, expressed in the relationships assumed between the variables. At last, the new values of the four variables may be such that they are again compatible with one another, and "the situation calls for no further adjustments."

The crux of the matter is that the addition of another variable, somehow related to one or more of the others, would change the picture. The magnitudes in which A, B, C and D are mutually compatible when they are the only players in the game may constitute serious incompatibility when they are joined by another player, say E, of a certain size. But another addition, say F, may neutralise the "disturbing " effect of E, and A, B, C, D in their " present " magnitudes may again be compatible and " everything could go on as it is." One cannot overemphasise this relativity of compatibility and incompatibility regarding extra variables included in, or excluded from, the selected set. Only a complete enumeration of the variables selected and interrelations assumed makes it meaningful to assert their mutual compatibility or incompatibility, that is, the equilibrium or disequilibrium of the chosen set. And, while a specification of the selected variables and assumed interrelations is required for every model and every problem, the definition of equilibrium and disequilibrium must not narrow the freedom of choice."

-F. Machlup, Equilibrium and Disequilibrium: Misplaced Concreteness and Disguised Politics,The Economic Journal, Vol. 68, No. 269. (Mar., 1958), pp. 1-24.[highlights mine]